"Multislice" generally refers to a technique used in medical imaging, particularly in computed tomography (CT) scans. Multislice or multi-detector CT (MDCT) technology involves the use of multiple rows of detectors within the CT scanner. This allows for the acquisition of multiple slices of images in a single rotation of the imaging system, which significantly improves the speed of image acquisition and enhances image quality.
The Nahm equations are a set of differential equations that describe the behavior of certain types of mathematical and physical objects, particularly in the context of supersymmetry and gauge theory. They were introduced by Werner Nahm in the context of solitons and are particularly relevant in the study of BPS (Bogomolny-Prasad-Sommerfield) states in supersymmetric theories.
Nambu mechanics is a theoretical framework in classical mechanics that generalizes the standard Hamiltonian and Lagrangian methods. It was developed by Yasunori Nambu in the 1970s as a way to describe systems with constraints and to deal with more complex types of motion. In Nambu mechanics, the equations of motion are formulated using a Nambu bracket, which is an extension of the Poisson bracket used in Hamiltonian mechanics.
Pontifex is a project associated with the development of a decentralized, blockchain-based system for addressing challenges in governance, community engagement, and decision-making. It often focuses on improving transparency, accountability, and efficiency within organizations or communities. The project may involve creating tools for voting, proposals, and civic participation that are secure and verifiable through blockchain technology.
The Superiority and Inferiority Ranking Method is a quantitative decision-making technique commonly used in multi-criteria decision analysis. It helps evaluate and rank alternatives based on multiple criteria by comparing them. Here's a breakdown of how the method works: ### Superiority Ranking 1. **Definition**: This aspect of the method involves assessing how much better one alternative is compared to others concerning specific criteria. 2. **Evaluation**: Each alternative is compared pairwise.
A traffic model is a mathematical or computational representation used to analyze, predict, and optimize the flow of traffic within a given area. Traffic models can be applied in various contexts, including urban planning, transportation engineering, and traffic management systems. Here's a breakdown of the main aspects of traffic models: 1. **Types of Traffic Models**: - **Macroscopic Models**: These provide a broad overview of traffic behavior by considering aggregate characteristics such as traffic flow, density, and speed.
Probability theory paradoxes refer to situations or scenarios in probability and statistics that lead to counterintuitive or seemingly contradictory results. These paradoxes often challenge our intuitive understanding of probability and highlight the complexities and nuances of probabilistic reasoning.
Symmetry is a concept that refers to a consistent and balanced arrangement of elements on either side of a dividing line or around a central point. It is a fundamental principle in various fields, including mathematics, physics, art, and nature. Here are a few ways symmetry can be understood: 1. **Mathematics**: In geometry, symmetry pertains to shapes and figures that remain invariant under certain transformations like reflection, rotation, or translation.
"All horses are the same color" is a statement that often refers to a notion introduced in a famous proof by induction and is often used as a humorous example of a flawed argument. The argument is typically presented in a mathematical or logical context to demonstrate the pitfalls of induction.
Differential topology is a branch of mathematics that studies the properties of differentiable functions on differentiable manifolds. It combines concepts from topology and differential calculus to explore and characterize the geometric and topological structures of manifolds. Key concepts in differential topology include: 1. **Manifolds**: These are topological spaces that locally resemble Euclidean space and allow for the use of calculus.
The Royal Dutch Mathematical Society, known as "Koninklijke Hollandse Maatschappij der Wetenschappen" in Dutch, is an organization dedicated to the promotion and advancement of mathematics in the Netherlands. Founded in 1752, it is one of the oldest mathematical societies in the world. The society serves as a platform for mathematicians to collaborate, share research, and promote mathematical education and outreach.
The C-theorem is a important result in theoretical physics, particularly in the context of quantum field theory and statistical mechanics. It is related to the renormalization group (RG) and the behavior of systems as they undergo changes in scale. In simple terms, the C-theorem provides a way to describe the flow of certain quantities (known as "central charges") in quantum field theories, particularly in two-dimensional conformal field theories.
Chiral symmetry breaking is a fundamental concept in particle physics and field theory, particularly in the context of quantum field theories that describe the strong interactions, like Quantum Chromodynamics (QCD). To understand chiral symmetry breaking, it's important to grasp the concepts of chirality and symmetry in particle physics. ### Chirality Chirality refers to the "handedness" of particles, specifically fermions (such as quarks and leptons).
The Clebsch-Gordan coefficients for SU(3) describe how to combine representations of the group. SU(3) has a more complex structure than SU(2), and its representations can be labeled using a notation involving Young diagrams.
Scalar–tensor theory is a class of theories in theoretical physics that combines both scalar fields and tensor fields, typically used in the context of gravity. The most well-known example of a scalar-tensor theory is Brans-Dicke theory, which was proposed to extend general relativity by incorporating a scalar field alongside the standard metric tensor field of gravity.
Conformal Field Theory (CFT) is a quantum field theory that is invariant under conformal transformations. These transformations include dilatations (scaling), translations, rotations, and special conformal transformations. The significance of CFTs lies in their mathematical properties and their applications in various areas of physics and mathematics, including statistical mechanics, string theory, and condensed matter physics.
Cointerpretability is a concept that generally arises in the context of interpreting two or more models or systems in relation to each other. While there isn't a universally standardized definition across all fields, it typically refers to the idea that the interpretations of different models can be understood in conjunction with one another, providing complementary insights or perspectives. In more technical settings, particularly in machine learning and AI, cointerpretability may involve assessing how well different models explain the same underlying phenomena or share features.
A Euclidean random matrix typically refers to a random matrix model that is studied within a Euclidean framework, often in relation to random matrix theory (RMT). Random matrices are matrices where the entries are random variables, and they are analyzed to understand their spectral properties, eigenvalues, eigenvectors, and various statistical behaviors.
"Five Equations That Changed the World" is a book by Michael Guillen that explores the significance of five mathematical equations that have had a profound impact on science, technology, and our understanding of the universe. The book aims to make complex mathematical concepts accessible to a wider audience by explaining how these equations have shaped modern thought and advanced human knowledge.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact